Signal to noise ratio of free space homodyne coherent optical communication after adaptive optics compensation

Designing and evaluating the adaptive optics system for coherent optical communication link through atmosphere requires to distinguish the effects of the residual wavefront and disturbed amplitude to the signal to noise ratio. Based on the new definition of coherent efficiency, a formula of signal to noise ratio for describing the performance of coherent optical communication link after wavefront compensation is derived in the form of amplitude non-uniformity and wavefront error separated. A beam quality metric is deduced mathematically to evaluate the effect of disturbed amplitude to the signal to noise ratio. Experimental results show that the amplitude fluctuation on the receiver aperture may reduce the signal to noise ratio about 24% on average when Fried coherent length r0=16 cm.